Problem: If $x \veebar y = 4x^{2}+y^{2}$ and $x \bigtriangleup y = 4x^{2}-y^{2}$, find $(-3 \bigtriangleup -6) \veebar -2$.
Solution: First, find $-3 \bigtriangleup -6$ $ -3 \bigtriangleup -6 = 4(-3)^{2}-(-6)^{2}$ $ \hphantom{-3 \bigtriangleup -6} = 0$ Now, find $0 \veebar -2$ $ 0 \veebar -2 = 4(0^{2})+(-2)^{2}$ $ \hphantom{0 \veebar -2} = 4$.